Henderson joined Saudi Arabia's Al Ettifaq from Liverpool in July before terminating his contract and signing for the Dutch side in January.
England manager Southgate was in the stands at Johan Cruyff Arena last month when the midfielder made his Ajax debut in a 1-1 draw with PSV in the Dutch league.
"It was nice to see that he (Southgate) is keeping an eye on me," Henderson told reporters on Wednesday ahead of Ajax's Europa Conference League last-16 match against Aston Villa.
"I've got to focus on my job here and if I'm doing that well and performing well then that gives me the best possible opportunity to get in the England squad.
"I definitely feel I can offer something to the national team. Of course I feel I can help the squad and the team going forward in the next camp and hopefully in the summer."
England are grouped with Slovenia, Denmark and Serbia at Euro 2024, which begins on June 14.
